面向小样本高维数据的秩检验非参控制图  

Nonparametric Control Chart of Rank Test for Small Samples of High-dimensional Data

作　　者：赵宇[1] 李艳婷[1] ZHAO Yu;LI Yanting(School of Mechanical Engineering,Shanghai Jiao Tong University,Shanghai,200240)

机构地区：[1]上海交通大学机械与动力工程学院,上海200240

出　　处：《中国机械工程》2022年第9期1104-1114,共11页China Mechanical Engineering

基　　金：国家自然科学基金(72072114)。

摘　　要：针对某些制造业质量数据存在的数据分布未知、数据维度高、受控样本少等特点,提出一种基于高维秩检验的多元非参数监控方案。通过生成观测值的秩矩阵并进行渐近秩变换,得到渐近秩变换检验数T_(n)^(*);基于检验数T_(n)^(*)设计具有滑动窗口的EWMA控制图,即HREWMA控制图。通过马尔可夫链对HREWMA控制图在不同条件(样本维度,均值漂移程度,受控样本量以及观测数据的分布)下的检测效果进行研究,并和其他多元非参控制图(DFEWMA、SREWMA、SSEWMA、RTC)进行对比,结果显示,对于检测具有大漂移的高维数据,HREWMA控制图的监控效果表现更优秀;在非正态数据的情况下,HREWMA控制图同样具有良好的监控效果。In view of the characteristics of some production data of manufacturing companies:unknown data distribution,high data dimensions,and few controlled samples,a multivariate nonparametric data monitoring program was proposed based on high-dimensional rank test.The asymptotic rank transformation test number T_(n)^(*) was obtained by generating the order of observations and the asymptotic rank transformation.A new EWMA control chart with sliding window(HREWMA)was designed based on the test number T_(n)^(*).The Markov chain was used to study the control effectiveness of the HREWMA control chart under different conditions(the sample dimension,the mean shift,the controlled sample size and the distribution of the observation data).Compared with other multivariate non-parametric control charts(DFEWMA,SREWMA,SSEWMA,RTC),the results show that for detecting high-dimensional data with large drift,the performance of HREWMA control chart is better;in the case of non-normal data,HREWMA control chart also has a good performance.

关 键 词：高维度 非参数 秩检验 渐近秩变换 多元指数移动平均 

分 类 号：TP277[自动化与计算机技术—检测技术与自动化装置]